Question

Expand the function f(x) = x^2 in a Fourier sine series on the interval 0 ≤ x ≤ 1.

Answer #1

Fourier Series
Expand each function into its cosine series and sine series for
the given period
P=2
f(x) = x, 0<=x<5
f(x) = 1, 5<=x<10

Fourier Series Expand each function into its cosine series and
sine series for the given period P = 2π f(x) = cos x

1. Find the Fourier cosine series for f(x) = x on the interval 0
≤ x ≤ π in terms of cos(kx). Hint: Use the even extension.
2. Find the Fourier sine series for f(x) = x on the interval 0 ≤
x ≤ 1 in terms of sin(kπx). Hint: Use the odd extension.

Find the Fourier series of the function f on the given
interval.
f(x) =
0,
−π < x < 0
1,
0 ≤ x < π

Expand the given function in an appropriate cosine or sine
series.
f(x) =
π,
−1 < x < 0
−π,
0 ≤ x < 1

(a) expand f(x)=8, 0<x<3 into cosine series period 6
(b) expand f(x)=8, 0<x<3 into a sine series period 6
(c) determine value each series converges to when x=42
(d) graph (b) for 3 periods, over the interval [-9,9]

Compute the complex Fourier series of the function f(x)= 0 if −
π < x < 0, 1 if 0 ≤ x < π
on the interval [−π, π]. To what value does the complex Fourier
series converge at x = 0?

Expand the Fourier Series.
f(x) = x|x|, -L < x < L, L > 0

Consider the first full period of the sine function:
sin(x), 0 < x < 2π.
(1) Plot the original function and your
four-term approximation using a computer for the range −2π < x
< 0. Comment.
(2) Expand sin(x), 0 < x < 2π, in a
Fourier sine series.

Find the Fourier Sine integral representation for the
function
f(x) = x, 0<x<a (and zero otherwise)

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